1. Field of the Invention
The present invention relates to method, apparatus, and computer program product for forming data to be analyzed by finite element method (FEM) by which displacement, temperature, and the like are analyzed and a calculation method based on finite element method.
2. Description of the Prior Art
According to the finite element method, the shape of an object which is an analysis target is divided into small units, a solution is sectionally approximated by a function having a finite value for every unit to calculate the solution of the entire shape. Hereinafter, the division of the entire shape into small units is referred to as xe2x80x9cmesh divisionxe2x80x9d, each unit thus obtained to as xe2x80x9celementxe2x80x9d, and an apex of an element to as xe2x80x9cnodal pointxe2x80x9d. The shape to be analyzed is defined by an assembly of element data and nodal point data, and these data are referred to as xe2x80x9cstructural dataxe2x80x9d.
In order to the form structural data, it is necessary to form the overall shape to be analyzed. A method of inputting the coordinates of all the apexes of the shape has been hitherto widely used to form the overall shape. However, this method has the disadvantage that it needs more time as an analysis target becomes three-dimensional and more complicated.
Therefore, JPA-6-4630 disclosed a method of combining fundamental shapes and local shapes which are registered in advance, thereby forming the overall shape. According to this method, the basic shapes and the local shapes are selected to input the actual dimensions, and the respective shapes of the basic shapes and local shapes are combined with one another, whereby the overall shape can be readily formed.
In order to form the structure data, a mesh dividing work is further needed. There have been hitherto known various techniques for supporting the mesh dividing work. For example, according to the method disclosed in JPA-6-4630, the overall shape of the assembled elements is automatically divided into hexahedral regions, such divisional numbers in the longitudinal, lateral and height directions that are equal between neighboring hexahedral regions are received from a user for every hexahedral regions, and the mesh division is performed on the basis of the divisional numbers. Further, according to the method disclosed in JPA-3-29057, the mesh division is automatically performed by a three-dimensional solid mesh generator, and each nodal point is moved by using a three-dimensional isoparametric smoothing method so that the shape of each element is well regulated. Still further, according to the method disclosed in JPA-5-108694, a similar shape model which is similar to a shape model to be analyzed and formed as an assembly of square blocks is generated, and it is projected onto the shape model (analysis target) to perform the mesh division. Any technique as explained above is based on the idea that the nodal points of the respective elements constituting the analysis target shape are coincident between neighboring elements.
As described above, it has been a dominant idea in the conventional techniques that the nodal points must be coincident between the neighboring elements. Therefore, when some fundamental shapes are combined to form the overall shape as disclosed in JPA6-4630, much time is needed for the mesh dividing work thereof. This is because a user must indicate the mesh divisional number so that the nodal points are coincident between neighboring areas.
Therefore, an object of the present invention is to provide a method for forming data to be analyzed by a finite element method, which can perform the work of forming the shape to be analyzed and of mesh division in short time.
Another object of the present invention is to provide a method for executing calculation based on a finite element method which can obtain a solution even when the nodal points are not coincident between elements.
According to one aspect of the present invention, there is provided a method for forming structural data to be analyzed by a finite element method which comprises steps of: providing structural elements having various shapes; inputting dimension for each of the structural elements; applying mesh generation to each of the structural elements, and piling up the structural elements irrespective of coincidence or non-coincidence of nodal points.
According to another aspect of the present invention, there is provided a calculation method based on finite element method for calculating nodal point displacement or nodal point temperature in case that structural data to be analyzed by a finite element method contain non-connected nodal points, which comprises a step of calculating the displacements or temperatures of non-connected nodal points of a structural element by using the displacements or temperatures of nodal points of the neighboring structural elements on the basis of constraint equations.
According to still another aspect of the present invention, there is provided an apparatus for generating input data to be analyzed by a finite element method, which comprises: a storage device which stores fundamental shapes; part data forming means for setting the actual dimension, the physical constants and the mesh dividing number for the fundamental shapes in accordance with a user""s instruction, thereby forming part data for the fundamental shapes; module data forming means for forming the data of a module on the basis of a pair of parts indicated by the user and the relative position between the parts in the pair, the module being constructed by a combination of the paired parts; analysis condition data forming means for forming analysis condition data according to the analysis condition indicated by the user; and data converting means for inputting model data comprising the part data, the module data and the analysis condition data, and forming an analysis model comprising structural data, converted analysis condition data and constraint equations, wherein the structural data comprises elements data and nodal points data which are obtained by building up the parts in accordance with the relative positions and then dividing the shapes of the parts by the mesh division number, each components of the converted analysis condition data corresponds to each nodal points, and the constraint equations connect non-connected nodal points between the parts.